I mean…how old is she? I expressed interest in joining the military in high school, too, after a recruiter souped me up after taking the ASVAB and scoring well. I ultimately decided against it for a variety of reasons. Many HS students cycle through a lot of careers and ideas before they settle on something they actually want to do.
I think the best strategy is taking a look at the military job chart and salary chart and showing her how much more she’ll make if she goes to college and becomes an officer, vs. going enlisted. The base pay for a brand-new E-1 is about $1600/month; the base pay for a brand new O-1 is over $3,000 a month. Officers are the managers and leaders in the military; she’ll hit a ceiling eventually as an enlisted member, and even the most senior enlisted member is still subordinate to the lowliest O-1 (although relationships are complex).
Moreover, one thing she may be surprised to know is that after a certain level as an enlisted member she’d be expected to get a bachelor’s degree anyway to continue to rise. When I met my husband’s chain of command at military functions, I was initially surprised to realize how many of them had bachelor’s and even master’s degrees. Take a look at the last several Chief Master Sergeants of the Air Force (and equivalent top-ranking enlisted personnel in the Army and Navy) - they all have BA/BS degrees, and some have master’s degrees.
So even if she wanted to be enlisted, a bachelor’s degree would benefit her in terms of pay and rank.
People make much of the “sergeant telling you when to wake up, what to do, and what to think” because they think basic training is representative of the entire experience of being in the military. Basic Military Training is only 6-8 weeks long. After that, many jobs in the military function a lot like a normal job - you wake up to make your shift, you’re told what to do in the context of your job, you can think what you want to think but you have some constraints on how you can express that (which is also true of non-military jobs).
Also, people in the military - as people outside - are different. There are 1.2 million active duty personnel in the U.S. Armed Forces. Not all of them are arrogant, obnoxious, or egotistical. That would be like assuming that everyone who works in the U.S. tech industry is arrogant, obnoxious, and egotistical.
I admit that I myself am biased because my husband’s a veteran (and service operations supporting the war in Iraq and Afghanistan), my grandfather’s a Korean War vet, and I’ve got cousins and uncles who have served or are currently serving as well.